I see that there are power steering pumps and reservoirs available for my RA29, but I'm not sure what else I might need to do to install power steering on my car.My Celica has the original R20 engine and hasn't been modified at all in regards to what's under the hood.

What else would I need to do to make this happen? Is it even possible?

Yes it will work with the 20R. The only other thing you would need is the bracket off a 20/22R/RE that has power steering for the pump. I haven't looked at mine in a while, but I believe that it replaces the air pump on your 20R. Should bolt right up to the 20R as they really didn't change the basic stuff on the block... yeah, yeah, yeah I know, they changed the deck height and the timing chain, blah, blah, blah... They didn't change the way the timing cover or most of the accessories mount to the front, so your bracket will bolt right up.